\ifnum\solutions=1 {
  \clearpage
} \fi
\item\subquestionpoints{5}
\textbf{Semi-supervised M-Step.}
Clearly state which are all the parameters that need to be re-estimated in the M-step. Derive the M-step to re-estimate all the stated parameters.  Specifically,
derive closed form expressions for the parameter update rules for $\mu^{(t+1)}$, $\Sigma^{(t+1)}$ and $\phi^{(t+1)}$ based on the semi-supervised objective.

\ifnum\solutions=1 {
  \input{04-semi_supervised_em/03-m-step-sol}
} \fi
